A Markovian Continuous Approximation Modeling for Batch Processing on a Single Machine

Batch processing is a common production approach used in a number of industries. In this work, we consider modeling approaches for performanceevaluation of system with batch processing and sequence-dependent setup times (between each job) on a single machine with Poisson arrivals. Optimalprocessing of each individual batch can be naturally formulated as a traveling salesman problem which makes overall system analysis difficult. Wepropose a semi-Markov process that is based on a continuous approximation modeling approach that can provide probability distributions for thesystem performance measures, without making explicit assumption on batch processing distribution. The model is validated against Monte-Carlo simulation.We also demonstrate how the model can be employed with illustrative use cases